Cambridge Essentials Mathematics Core 9 GM1.1 Homework
/ GM1.1 Homework1The diagram show four quadrilaterals.
aWhich quadrilateral is concave? Explain how you decided.
bRyan says that shape A is a regular polygon because all the sides are equal.
Is he correct? Explain your answer.
cJosh says that shape D is a regular polygon because all the angles are equal.
Is he correct? Explain your answer.
dBen disagrees with both Ryan and Josh and says that shape B is the regular polygon.
Is Ben correct? Explain your answer.
aHow many triangles is the hexagon divided into?
bComplete this statement.
The sum of the interior angles of any hexagon is _____ × 180° = _____°. /
cUse your answer to part b to work out the marked angle in each of these polygons.
iiiiii
3Ravi measures the ten interior angles of decagon. He writes down only nine of the angles.
140°, 160°, 138°, 157°, 175°, 129°, 150°, 144°, 162°
Work out the size of the tenth angle.
4Use the formula (n – 2) × 180° to find the interior angle of
aa regular octagon
ba regular 20-sided polygon.
5The diagram shows the seven interior angles of a heptagon and one of its exterior angles.aWrite the size of each exterior angle on the diagram.
bFind the sum of the exterior angles.
cComplete this sentence:
The sum of the exterior angles of any polygon is always ______. /
6For each regular polygon calculate
ithe exterior angle
iithe interior angle.
a18 sidesb10 sidesc30 sidesd6 sides
7If the interior angle of a regular polygon is 150°, calculate
ithe exterior angle
iithe number of sides the polygon has.
8Jade says that it is possible to have a regular polygon with an interior angle of 156° if the exterior angle is 24°.Is she correct? If so, how many sides does the polygon have?
9ABCDEF is a hexagon.aFind the size of angle a.
Give a reason for your answer.
bFind the size of angle b.
Explain how you worked it out.
cFind the size of angle of c.
Give a reason for your answer. /
dDan says that angle d is 80°.
Is this true? Explain your answer.
eEmma says that angle e is 60° because AB is parallel to FC, so it is an alternate angle. Is she correct?
fIs the line FC parallel to ED?
Explain how you decided.
gFind angle g.
Give a reason for your answer.
hIs the hexagon ABCDEF a regular polygon?
Explain your answer.